Statistical mechanics of permanent random atomic and molecular networks: Structure and heterogeneity of the amorphous solid state

TL;DR

This paper develops a statistical-mechanical framework to analyze the structure and heterogeneity of amorphous solid networks formed by permanent random covalent bonds, providing analytical solutions near the transition point.

Contribution

It introduces a comprehensive analytical approach to characterize local structural heterogeneity and order parameters in amorphous solids formed by random covalent bonding.

Findings

Positional localization matches vulcanized media results.

Derived order parameters for positional and orientational freezing.

Analytical solutions valid near the amorphous solidification transition.

Abstract

Under sufficient permanent random covalent bonding, a fluid of atoms or small molecules is transformed into an amorphous solid network. Being amorphous, local structural properties in such networks vary across the sample. A natural order parameter, resulting from a statistical-mechanical approach, captures information concerning this heterogeneity via a certain joint probability distribution. This joint probability distribution describes the variations in the positional and orientational localization of the particles, reflecting the random environments experienced by them, as well as further information characterizing the thermal motion of particles. A complete solution, valid in the vicinity of the amorphous solidification transition, is constructed essentially analytically for the amorphous solid order parameter, in the context of the random network model and approach introduced by Goldbart and Zippelius [Europhys. Lett. 27, 599 (1994)]. Knowledge of this order parameter allows us to draw certain conclusions about the stucture and heterogeneity of randomly covalently bonded atomic or molecular network solids in the vicinity of the amorphous solidification transition. Inter alia, the positional aspects of particle localization are established to have precisely the structure obtained perviously in the context of vulcanized media, and results are found for the analogue of the spin glass order parameter describing the orientational freezing of the bonds between particles.